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Search: id:A135586
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| A135586 |
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a(1)=0; for n >= 1, a(2n)=a(n)+2^A000120(n)-1, a(2n+1)=2a(2n). |
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+0
3
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| 0, 1, 2, 2, 4, 5, 10, 3, 6, 7, 14, 8, 16, 17, 34, 4, 8, 9, 18, 10, 20, 21, 42, 11, 22, 23, 46, 24, 48, 49, 98, 5, 10, 11, 22, 12, 24, 25, 50, 13, 26, 27, 54, 28, 56, 57, 114, 14, 28, 29, 58, 30, 60, 61, 122, 31, 62, 63, 126, 64, 128, 129, 258, 6, 12, 13, 26, 14, 28, 29, 58, 15, 30
(list; graph; listen)
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OFFSET
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1,3
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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If n=2^{e_{k-1}}+ ... +2^{e_1}+2^{e_0}, where k=A000120(n) and e_{k-1}> ... >e_1>e_0, then a(n)=e_0+2e_1+ ... +2^{k-1}e_{k-1}.
a(2^k) = k; a(4*k+2) = a(4*k+1) + 1; a(4*k+3) = 2*a(4*k+2). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 02 2008
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MAPLE
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b:=proc(n)if n=0 then 0 elif `mod`(n, 2)=0 then b((1/2)*n) else b((1/2)*n-1/2)+1 end if end proc: a:=proc(n) if n=1 then 0 elif `mod`(n, 2)=0 then a((1/2)*n)+2^b(n)-1 else 2*a(n-1) end if end proc: seq(a(n), n=1..60); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 02 2008
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MATHEMATICA
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a = {0}; For[n = 2, n < 80, n++, If[OddQ[n], AppendTo[a, 2*a[[ -1]]], AppendTo[a, a[[n/2]] + 2^Length[Select[IntegerDigits[n/2, 2], # == 1 &]] - 1]]]; a - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 02 2008
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CROSSREFS
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Cf. A135587, A000120, A135533.
Adjacent sequences: A135583 A135584 A135585 this_sequence A135587 A135588 A135589
Sequence in context: A127968 A037026 A116651 this_sequence A116646 A091188 A127712
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KEYWORD
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nonn,easy
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AUTHOR
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D. E. Knuth, Mar 01 2008
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EXTENSIONS
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More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Emeric Deutsch (deutsch(AT)duke.poly.edu) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 02 2008
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